The manufacture of nanocrystalline toroidal cores, i.e. of soft-magnetic toroidal cores, at least 50% of the material volume of which is taken up by fine crystalline particles having a particle size of 100 nanometers or less, is generally difficult and costly because the magnetic material, for example, must be nearly free of magnetostriction after thermal treatment and, in addition to this, virtually no mechanical tension must be allowed to effect the magnetic material during thermal treatment. It is therefore desirable to provide a method for manufacturing magnetic cores that is less sensitive and easer to carry out, in order to thus achieve a more easily manufactured magnetic core.